Firemen said there were no known casualties so far, though a number of people were suffering minor respiratory problems from exposure to smoke.
The entire island is expected to be placed under a state of emergency and reports of arson are under investigation. Greek news agency ANA said the fires had started after a revolt by asylum seekers who were to be placed in isolation after testing positive for coronavirus or coming into close contact with an infected patient.
Government spokesman Stelios Petsas added that authorities faced a “titanic” effort to shelter asylum seekers rendered homeless by the blaze, as well as track down and isolate dozens of confirmed coronavirus infections among them.
“There are 35 positive cases and they need to be isolated… to prevent an outbreak among the local population,” Petsas told state TV ERT.
The camp has seen a spike in coronavirus patients since reporting its first case last Wednesday, with 35 confirmed infections so far.
Migrant camps on the islands have endured months of lockdowns as a result of the coronavirus pandemic, with access severely restricted.
But at Moria, the restrictions have been harder to enforce because of the large number of asylum seekers sleeping outside the camp’s walls.
Rights groups including the UN refugee agency have urged Greece to reduce congestion in its migrant camps.
The Moria camp, which was built to hold fewer than 2,800 people, had been routinely criticised for its lack of hygiene and overcrowding.
Many refugees have been unable to find lodgings and jobs after leaving the camps, with housing and cash benefits recently scaled back by the government.